摘要
提出了一种新的谱随机有限元分析方法——递推求解方法。讨论了已有的几种随机场的谱展式 ,提出将随机结构的随机响应表示成非正交多项式混沌展式 ,并证明了这个展式的收敛性。在此基础上将随机微分方程表示成了和摄动法类似的一系列确定的递推方程 ,这些递推方程可用确定性有限元方法求解。该方法比在正交多项式混沌基上投影并取期望的方法更简洁实用 ,更适合大规模有限元的求解。该方法同样能解决有较大随机涨落的力学问题。
A new spectral stochastic finite element method to solve mechanical problems involving material variability and random load is proposed. In this paper,this method is called recursive stochastic finite element method. After Karhunun-loeve expansion,hermite polynomials chaos and askey chaos are introduced,nonorthogonal polynomials chaos is given to express a general second-term random process and its convergence is approved. The control equations of random mechanical problem can be formed using FEM,which are matrix equations containing many uncorrelated random variables. Then a series of deterministic recursive equations are set up through nonorthogonal polynomials in the same order. This method is very similar to the perturbation method,it can solve static problem including random variables of large fluctuation levels. Comparing this with spectral stochastic finite element method,this method is more suitable for solving large dimensions′ mechanical problem.
出处
《武汉理工大学学报》
CAS
CSCD
2004年第5期42-44,51,共4页
Journal of Wuhan University of Technology
基金
国家自然科学基金 (5 0 2 0 80 16 )
关键词
谱随机有限元
非正交多项式混沌
递推求解方法
spectral stochastic finite element method
nonorthogonal polynomials chaos
recursive stochastic finite element method
